Data-Driven Synthesis of Safety Controllers for Partially-Observable Systems with Unknown Models

This paper is concerned with the formal synthesis of safety controllers for partially-observable discrete-time control systems with unknown mathematical models. Given a state estimator with unknown dynamics but a known upper bound on the estimation error, we propose a data-driven approach to compute controllers that render the partially-observable systems with unknown dynamics safe. Our proposed method is based on the construction of control barrier certificates, where we first formulate the barrier-based safety problem as a robust program (RP). The proposed RP is not tractable since the unknown model of the estimator appears in one of its constraints. To tackle this issue, we collect a set of data from the black-box system and its estimator and replace the original RP with a scenario program (SP). Due to the existence of a max-min constraint in the SP, we construct an analogous scenario program, denoted by SP
^α
, in which the max-min constraint is replaced with a single inequality constraint. The control barrier certificates together with their corresponding controllers can then be computed by solving SP
^α
via the collected data. By connecting the feasible solutions of SP
^α
and SP, the safety of the partially-observable system equipped with the synthesized controller can be guaranteed with 100% confidence. We show the effectiveness of our results by synthesizing a safety controller for a partially-observable Van der Pol oscillator with unknown dynamics.